In electron optics various devices are available for the focusing, deflection, and mass and energy analysis of electrons and ions and these devices have been comprehensively described in various works on the subject of electron optics. Nearly all electron optical devices suffer from aberrations and the most serious of these aberrations is usually what has been called aperture defect. Aperture defect is present when electrons leaving a source on the optical axis of a device, at a relatively large angle to the axis, (the so-called peripheral trajectories) re-cross the axis or come to a focus on the axis at shorter or a longer distance from the source than those leaving the source at a small angle to the said axis (the so-called paraxial trajectories). The angles generally encountered in practical electron optics are generally significantly smaller than those used in visible light optics. For instance 10.degree. is a large angle in electron optical terms whereas 45.degree. is common in light optics. The aperture defect in an axially symmetrical electron lens is generally known as spherical aberration. In a lens of planar symmetry it has been called "linear aberration coefficient". Each type of deflection energy analyzer suffers from a similar defect even though it may have a curved optical axis, defined as the path of the median optical ray. Other types of aberration also exist in charged particle optical systems, but in the following the word aberration will be taken to represent the aperture defect.
The effect of the aberration in an energy analyzer is to limit the energy resolution of the device whereas in lenses the aberration limits the image quality or the smallness of image.
Various means for reducing the spherical aberration of an axially symmetric electron lens have been proposed and successfully used (see for instance the article by A. Septier entitled `The Struggle to Overcome Spherical Aberration in Electron Optics` in `Advances in Optical and Electron Microscopy` 1966 Vol I, p204 et seq). However, particularly in the case of cylindrical and hemispherical (or other section of a sphere) electrostatic energy analysers, the problem of reducing the aberration still remains.